SAR as such is a well-known technology, by which it is possible with a radar device mounted on a moving platform to obtain a much finer angular resolution of the stationary ground than will be furnished by the radar antenna. This refinement is achieved by storing radar data over a length of time and adopting the fact that during this time the radar has registered the ground from many different positions. A SAR processor mathematically transforms these radar data into a SAR image of the ground, which has the angular resolution of an antenna aperture, corresponding to the flight path along which data were stored.
The SAR radar located on a platform e.g. on an aircraft or a satellite moves along a nominal straight path and illuminates a large ground area by means of an antenna. High range resolution pulses are transmitted from the antenna and the return signal from the ground is received by the antenna and recorded along the straight path. By signal processing, high resolution is accomplished both along and transversely of the straight path. A condition for this is that the position of the antenna is known or can be calculated within a fraction of the resolution and that the amplitude and phase of the transmitted and received radar signals are known.
FIGS. 1a and 1b illustrate the fundamental ambiguity of SAR as regards moving targets on ground.
The description uses polar coordinates instead of, as is more common, Cartesian coordinates. By a moving target is henceforth meant an object moving across the ground, the object being known as regards its general properties, e.g. radar cross section order of magnitude and its general pattern of motion, but its actual presence and state of motion are to be determined by the radar measurement. A moving target can as a special case be stationary, with its velocity relative to ground being zero. Henceforth in the description a moving target is including also this special case.
The diagram in FIG. 1a, with an x-axis 101 and a y-axis 102, shows with a first arrow 103 the trajectory of a stationary ground point and with a second arrow 104 the trajectory of a moving target, which are mapped into the same pair, R,Φ, of SAR image polar coordinates. The two trajectories differ by a rigid rotation φ around a z-axis in the rest frame of the SAR platform being located at the origin 105. The axes symbol 108 illustrates the different axes including the z-axis. FIG. 1a thus illustrates movements of ground targets relative a fixed SAR platform. The SAR platform can equally well be considered moving relative ground in the direction of the X-axis 101. The y-axis 102 is thus perpendicular to the path of the SAR-platform. A moving target being located at a true position 106 with polar coordinates R,Φ−φ, at time T=0, will during the SAR processing be misplaced and located at an apparent position 107 having polar coordinates R,Φ. In FIG. 1a the angle φ is negative as the true position 106 is oriented in negative angle direction, i.e. anti-clockwise, in relation to the apparent position 107. These facts are known and fundamental basis for SAR processing.
FIG. 1b is a vector diagram with velocity in the direction of the movement of the SAR platform on an {dot over (x)}-axis 110 and velocity in a perpendicular direction on an {dot over (y)}-axis 111. The axes symbol 118 shows the different velocity axes, {dot over (x)}, {dot over (y)} and ż with velocities in the x, y and z directions. FIG. 1b shows a velocity vector 112 of a moving target in the ground frame, i.e. the movement relative to the ground. A moving target velocity vector 117, with velocity in relation to the SAR platform, will have its end point on a circle 113 of diameter 2V, V being the velocity of the moving SAR platform relative to ground. A ground point velocity vector −V (in FIG. 1b shown as − V) represents the velocity of a ground point in relation to the moving SAR platform. Varying the processing velocity parameter V→W, and processing the SAR image to contain coordinates Φ outside the region of the antenna footprint any moving target will be depicted as having an apparent position in the SAR image at point R,Φ for the proper selection of W. With the processing velocity W the moving target velocity vector will lie on the dotted circles 114-116 in FIG. 1b. The angle φ is the rigid rotation shown also in FIG. 1a. When the angle φ becomes zero the velocity in the y-direction will be zero.
It is regarded as a known fact that SAR information is ambiguous in the described sense that not only a fixed point on the ground surface (which may correspond to some feature of a parked vehicle for instance), but an entire class linear movements on the ground all maps into the same particular point on the SAR image.
This ambiguity, which is basic to the invention, can be stated mathematically as follows:
Assume a flat ground plane and an aircraft uniformly moving along a rectilinear path parallel to the ground. Capital letters are used for polar coordinates in the ground plane to represent fixed ground points. The SAR image is thus a function ƒ(R,Φ) assigning an amplitude to each ground point R,Φ. Radar data is represented F(r,t), where r is 3-dimensional distance from the radar antenna phase centre to any point in 3-dimensional space and t is time.
The transformation between data and the SAR image is:
                              f          ⁡                      (                          R              ,              Φ                        )                          =                              ∫                          -              T                        T                    ⁢                                    F              ⁡                              [                                                                            r                                              R                        ,                        Φ                                                              ⁡                                          (                      t                      )                                                        ,                  t                                ]                                      ⁢                          ⅆ              t                                                          (        1        )            where 2T is radar registration time. Here rR,Φ(t) is the range history of the particular ground point R,Φ. ƒ(R,Φ) is the SAR-image.
The various methods of SAR processing are all different forms of approximations or re-expressions of the fundamental expression (1). The main reason for making such reformulations is to make the evaluation of expression (1) numerically expedient. Reformulations may also invoke extra considerations, such as compensation due to a non-uniformity of the platform path, undulations of the ground, conditions relating the radar antenna and so forth.
According to our assumptions, each ground point R,Φ will follow the path of uniform linear motion in the rest frame of the aircraft. ThusrR,Φ(t)=(R sin Φ−Vt)eX+R cos ΦeY+HeZ  (2)assuming the aircraft to be heading in the x-direction (all coordinates will be in the SAR platform frame—upper case letters refer to the position of moving targets at time zero and other motion constants, lower case letters to coordinates and variables in general, letters in bold represents vectors, ex, ey and ez are basis vectors in x, y and z directions. The polar coordinates R,Φ are defined in FIG. 2 with the basis vectors defining the axes in space. The polar coordinate angle Φ is thus an angle in clockwise direction starting from the ey-axis. The quantity H is the platform altitude over ground and will be assumed constant and known just as the platform velocity V, t is time. Then rR,Φ(T)=|rR,Φ(t)| which is the absolute value of the rR,Φ(t)-vector, so the range history isrR,Φ(t)=√{square root over ((R sin Φ−Vt)2+R2 cos2Φ+H2)}  (3)Expression (1) has a most important implication, namely that any target having the range history rR,Φ(t) will become located in the SAR image in R,Φ. Hence if there is an ambiguity (as there may be) in that several targets have the same range history rR,Φ(t), the responses from these targets will all be superimposed in R,Φ regardless of the actual target coordinates.
Such ambiguities arise in particular if there are moving targets. Assume that during the few seconds of integration time normally required for SAR, these move in a uniform fashion. Thus in the reference frame of the SAR platform the motion of a moving target can be representedrmover(t)=R sin ΦeX+R cos ΦeY+HeZ+(v−VeX)t  (4)where v is the moving target velocity relative to the ground. It is possible to test SAR data F(r,t) for the presence of a hypothetical moving target by applying the integration
                              f          ⁡                      (            mover            )                          =                              ∫                          -              T                        T                    ⁢                                    F              ⁡                              [                                                                            r                      mover                                        ⁡                                          (                      t                      )                                                        ,                  t                                ]                                      ⁢                          ⅆ              t                                                          (        5        )            
Tresholding the retrieved amplitude with respect to the noise statistics of a set of different moving target hypotheses, the presence of a moving target can be obtained with the desired degree of confidence as the retrieved amplitude will be considerably increased at the presence of a moving target. However, while it is possible to detect a moving target in this way, due to the aforementioned ambiguities it is not possible to estimate all the parameters of its motion.
The class of moving targets which all map into the response of a static ground point are easily determined. It is indeed seen that upon a rigid rotation of equation (2) around the z-axisr′R,Φ(t)=(R sin Φ−Vt)(cos φeX−sin φeY)+R cos Φ(sin φeX+cos φeY)+HeZ  (6)the range response (3) will not be altered. However, (6) may be re-writtenr′R,Φ(t)=R sin(Φ+φ)eX+R cos(Φ+φ)eY+HeZ+[V(1−cos φ)eX+V sin φeY−VeX]t  (7)
Comparing with equation (4), we find that any moving target with parameters:Rmover=R Φmover=Φ+φ{dot over (x)}mover=V(1−cos φ){dot over (y)}mover=V sin φ  (8)                where φ is arbitrary—will map by integral (5) into the same SAR image coordinates R,Φ. In particular φ=0 corresponds to that R,Φ is a static point scatterer, see FIG. 1b. The non-noticeable states of motion have velocity vectors lying on a circle in the {dot over (x)},{dot over (y)}-plane with centre at {dot over (x)}=V, {dot over (y)}=0 and diameter 2V (cf. FIGS. 1 and 3).        
It is thus possible, for instance, that a vehicle seen in the SAR image, is not at all in the state of remaining stationary at the position apparent from this image, but is actually moving during the registration time. It is a property of the SAR image that such a moving target becomes misplaced in the SAR image, i.e. the true track of the moving vehicle can be quite separated from its apparent position in the SAR image. This is illustrated in FIG. 3. FIG. 3 shows the apparent position 301 of a moving target in a SAR-image at R,Φ. The angle Φ is here negative as it is oriented in anti-clockwise direction from the y-axis. The angle φ is positive in FIG. 3, in contrast to FIG. 1a, as the true position 302 here is oriented in positive angle direction, i.e. clockwise, in relation to the apparent position 301. The true position 302 of the moving target is located at R,Φ+φ as explained in association with FIG. 1a. The SAR platform with the antenna is located at some point 303 along the z-axis. The antenna footprint 304 on the ground, i.e. the area on the ground illuminated by the antenna, is illustrated as an area with a line pattern in FIG. 3. In the example of FIG. 3 the true position of the moving target will thus be moved to an apparent position in the SAR image outside the antenna footprint. The SAR image coordinates R,Φ and the true position R,Φ+φ are related by the angle φ, which together with the velocity parameter W determine the ground velocity vector. The SAR image containing moving targets is seen to take the shape of a first angular sector 305 shown without a line pattern, which spreads an angle of approximately 10°, corresponding to a maximum value of φ for ground velocity <50 m/s and a SAR platform ground velocity of 300 m/s. This can be calculated from expression (8) which gives that the velocity of the moving target in relation to the ground, in this example 50m/s, divided with the velocity of the SAR platform in relation to ground, in this example 300m/s approximately equals φ in radians. In this example the velocity ratio becomes 1/6, which thus corresponds to φ being 1/6 of a radian or 10 degrees. The maximum width of the first angular sector 305, in this example, is thus 10 degrees valid for true positions of moving targets positioned at the borderline of the antenna footprint. The angle φ in FIG. 3 is exaggerated for clarity reasons. For velocities in the opposite direction the spread will for the same reasons result in a second angular sector 306. Within, the sector covered by the antenna footprint 304, which contains the ground clutter, a relatively high SAR resolution is required for moving targets to exhibit sufficient clutter SNR (Signal to Noise Ratio) with respect to the ground clutter in the SAR image. Outside the clutter area, i.e. in the first 305 and the second 306 angular sectors the SAR image is free from ground clutter and moving target detection can be obtained at lower SAR resolution. Detection at such lower resolution allows data to be reduced after which improved resolution and moving target parameter accuracy can be achieved with small processing effort.
Since moving targets typically move at velocities an order of magnitude smaller than the aircraft velocity V it follows from expression (8), and is plainly seen in FIG. 1b, that these moving targets must move in a direction close to the y-direction in order to appear as misplaced stationary ground features in the SAR image. The angle φ will thus be just a few degrees. It may still correspond to a significant misplacement of the moving target in the SAR image since the distance from the radar to the target can be large.
For moving targets discussed so far the accumulated signal energy backscattered from the target into the radar will correspond to the intensity of the target in the SAR image. Generally targets will not move in such a way that they only cause misplacement effects in the SAR image. In the general case, the moving targets will be defocused in the sense that they appear smeared and with lower intensity in the SAR image as compared to cases when they are focused, i.e. the cases discussed so far. Thus generally moving targets will be both misplaced and defocused.
Particularly, if ground targets move in the x-direction at slow velocities they will be defocused. This defocusing effect is significantly less strong than the misplacement effect, and will not be noticeable when resolution is coarse. This means that targets slowly moving in the x-direction remain focused if the resolution is coarse. For high resolution SAR such a motion may however have the effect of making targets defocused to such a degree that they become invisible in the SAR image.
A special version of SAR, so-called GMTI, relies on this effect, viz. that at coarse SAR resolution moving targets remain focused, though they are generally misplaced. GMTI is the established method to detect and position moving targets. GMTI uses several radar channels, related to different phase centres distributed over the actual radar antenna. Any location on the ground will correspond to a certain phase shift between the phase centres. By using two such channels it is thus possible to cancel the ground response coming from any particular point on the ground. By using the GMTI channels to produce a combined SAR image which cancels the ground response at some point on the ground, will cause a moving target being positioned by the SAR process to this point to have a true position somewhere where the ground return cancellation does not apply. Thus it will be highlighted in the combined SAR image. Providing the same combined SAR image for two further channels, the true position of the highlighted moving target can be determined.
In most of the modern SAR-systems, GMTI and high resolution SAR (HR SAR) are used as a combined pair of methods to focus both stationary and moving targets. HR SAR is defined as a SAR system having an operating frequency above 1 GHz and a resolution of approximately less than one meter. The combination fails however in providing a complete situation picture.
A major shortcoming of the GMTI is that the method is based on coarse resolution SAR images. In typical GMTI applications, several targets may be situated within the same resolution cell and for this reason it will not be possible to preserve moving target individuality when the moving targets pass each other at close ranges.
Furthermore, due to the coarse resolution of GMTI, the ground response must be eliminated for the moving target to be detectable at all. Since for motion along paths parallel to the track of the aircraft there is no misplacement between stationary ground and moving targets, targets moving in this way are thus not possible to detect by GMTI. At the same time they may well be defocused and not visible with HR SAR, if the velocity of the moving target is outside the resolution. For motion at right angles to the aircraft track misplacements are large also at moderate moving target velocities enabling efficient ground cancellation and good GMTI performance. However, when the velocity of the moving target is sufficiently small (for instance when the moving target is in a process of stopping or starting) GMTI will not work.
HR SAR has poor performance with respect to moving targets. When SAR resolution is very high, even very small velocity fluctuations will make the targets strongly defocused, or even invisible. Since targets in the process of stopping or starting must change velocity they will always be out of focus and quite likely invisible in HR SAR.
U.S. Pat. No. 6,441,772 B1 discloses a Low frequency SAR radar system. The invention describes a method to process SAR data with so called Fast Factorized Back projection (FFB) and a solution for detecting moving targets. The method proposed in U.S. Pat. No. 6,441,772 B1 is based on FFB for SAR focusing of linearly moving targets, incorporating FFB SAR imaging of the stationary ground as a special case. For stationary ground the method of U.S. Pat. No. 6,441,772 B1 works very well. However there is still a need for an improved method for detecting moving targets.
In summary, current technology provides a ground situation picture which has shortcomings as regards moving targets. The shortcomings are:                poor target tracking capability,        targets in certain states of motion will not be detected, and        the detection ability for moving targets starting or stopping is very poor or non existing.        
There is thus a need to achieve a method, a Radar System and a SAR processor for improving the possibility to detect moving targets with respect to the above mentioned shortcomings in particular to preserve moving target individuality during tracking of multiple targets moving in the vicinity of each other.